In rectangle ABCD, the diagonals meet at point O. Find side BC if the perimeter of triangle AOD is 18 cm and AC + BD = 22 cm.
AC and BD are the diagonals of the rectangle, which means they are equal and intersect in the middle. Find half of the diagonal (segment AO):
AC = 22/2 = 11 cm;
AO = AC / 2 = 11/2 = 5.5 cm;
AO = OD;
Let’s find the unknown side of the triangle AOD:
AD = 18 – 5.5 – 5.5 = 7 cm;
This side of the rectangle is opposite to the BC side, and the opposite sides of the rectangles are equal.
Answer: BC = 7 cm.
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